Determine the points of intersection using the parabola's equation. Use these points to write the equation of the line in slope-intercept form.
B
Practice makes perfect
We are asked to write an equation of the line bounding the tabletop. To do so, let's find the coordinates of the points of intersection of the line and the parabola and then use them to write the equation of the line.
Points of Intersection
We know that the parabola and the line intersect when x= - 1 and when x= 3. The points of intersection are the points common to both the parabola and the line. Therefore, to find the y-coordinates of these two points we will use the function that models the parabola.
y=2x^2-3x+2
First, let's determine the y-value for x= - 1!
Recall that exactly one line passes through two points. Therefore, given two points of intersection we are able to write an equation of the line. We will write the equation of the line in slope-intercept form.
y=mx+b
Here, m is the slope and b is the y-intercept. Let's use the Slope Formula to find the slope m of the line bounding the table.
m=y_2-y_1/x_2-x_1
We will use the points of intersection, ( - 1,7) and ( 3,11), as the points (x_1,y_1) and (x_2,y_2).
The slope is equal to 1. Let's write a partial equation of the line.
y=1x+b ⇔ y=x+b
Now we will use one of the points to write an equation that can be solved for b. Let's use ( - 1, 7)!
